Calculation of repeatable control strategies for kinematically redundant manipulators

Includes bibliographical references (page 130).A kinematically redundant manipulator is a robotic system that has more than the minimum number of degrees of freedom that are required for a specified task. Due to this additional freedom, control strategies may yield solutions which are not repeatable in the sense that the manipulator may not return to its initial joint configuration for closed end-effector paths. This paper compares two methods for choosing repeatable control strategies which minimize their distance from a nonrepeatable inverse with desirable properties. The first method minimizes the integral norm of the difference of the desired inverse and a repeatable inverse while the second method minimizes the distance of the null vectors associated with the desired and the repeatable inverses. It is then shown how the two techniques can be combined in order to obtain the advantages of both methods. As an illustrative example the pseudoinverse is approximated in a region of the joint space for a seven-degree-of-freedom manipulator

Comparison of two methods for choosing repeatable control strategies for kinematically redundant manipulators, A

Includes bibliographical references.A kinematically redundant manipulator is a robotic system that has more than the minimum number of degrees of freedom that are required for a specified task. Due to this additional freedom, control strategies may yield solutions which are not repeatable in the sense that the manipulator may not return to its initial joint configuration for closed end effector paths. This paper presents two methods for choosing repeatable control strategies which minimize their distance from a non-repeatable inverse with desirable properties. The first method minimizes the integral norm of the difference of the desired inverse and a repeatable inverse. While this is the more appropriate criterion, it results in a difficult optimization. The second method, which minimizes the distance of the null vectors associated with the desired and the repeatable inverses, is somewhat easier to implement. As an illustrative example the pseudoinverse is approximated in a region of the joint space using both techniques.This work was supported by Sandia National Laboratories under contract number I8-4379B. Additional support was provided by the NEC Corporation and the TRW Foundation

Near-pseudoinverse control of kinematically redundant manipulators with the constraint of repeatability

Includes bibliographical references (pages 119-120).The issue of repeatability is addressed for a particular redundant manipulator. This particular manipulator is a planar three-link manipulator with two orthogonal, prismatic joints and a third revolute joint. This manipulator can be thought of as a mobile robot with one revolute joint. It is shown that pseudoinverse control has no stable surfaces for this robotic manipulator. A class of repeatable inverses is then derived. Finally the repeatable inverse which is closest in an integral norm sense to the pseudoinverse is found from this class

A Feasibility Study on a Parallel Mechanism for Examining the Space Shuttle Orbiter Payload Bay Radiators

The goal of the project was to develop the necessary analysis tools for a feasibility study of a cable suspended robot system for examining the space shuttle orbiter payload bay radiators These tools were developed to address design issues such as workspace size, tension requirements on the cable, the necessary accuracy and resolution requirements and the stiffness and movement requirements of the system. This report describes the mathematical models for studying the inverse kinematics, statics, and stiffness of the robot. Each model is described by a matrix. The manipulator Jacobian was also related to the stiffness matrix, which characterized the stiffness of the system. Analysis tools were then developed based on the singular value decomposition (SVD) of the corresponding matrices. It was demonstrated how the SVD can be used to quantify the robot's performance and to provide insight into different design issues

Analysis of eigendecomposition for sets of correlated images at different resolutions

Includes bibliographical references.Eigendecomposition is a common technique that is performed on sets of correlated images in a number of computer vision and robotics applications. Unfortunately, the computation of an eigendecomposition can become prohibitively expensive when dealing with very high resolution images. While reducing the resolution of the images will reduce the computational expense, it is not known how this will affect the quality of the resulting eigendecomposition. The work presented here gives the theoretical background for quantifying the effects of varying the resolution of images on the eigendecomposition that is computed from those images. A computationally efficient algorithm for this eigendecomposition is proposed using derived analytical expressions. Examples show that this algorithm performs very well on arbitrary video sequences.This work was supported by the National Imagery and Mapping Agency under contract no. NMA201-00-1-1003 and through collaborative participation in the Robotics Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0012

A Kinematic Analysis and Evaluation of Planar Robots Designed From Optimally Fault-Tolerant Jacobians Khaled M. Ben-Gharbia, Student Member, IEEE,

Abstract—It is common practice to design a robot’s kinematics from the desired properties that are locally specified by a manipulator Jacobian. In this work, the desired property is fault tolerance, defined as the postfailure Jacobian possessing the largest possible minimum singular value over all possible locked-joint failures. A mathematical analysis based on the Gram matrix that describes the number of possible planar robot designs for optimally fault-tolerant Jacobians is presented. It is shown that rearranging the columns of the Jacobian or multiplying one or more of the columns of the Jacobian by ±1 will not affect local fault tolerance; however, this will typically result in a very different manipulator. Two examples, one that is optimal to a single joint failure and the second that is optimal to two joint failures, are analyzed. This analysis shows that there is a large variability in the global kinematic properties of these designs, despite being generated from the same Jacobian. It is especially surprising that major differences in global behavior occurs for manipulators that are identical in the working area. Index Terms—Fault-tolerant robots, robot kinematics, redundant robots. I

Computational feasibility study of failure-tolerant path planning, A

Includes bibliographical references (page 239).This work considers the computational costs associated with the implementation of a failure-tolerant path planning algorithm proposed in [1]. The algorithm makes the following assumptions: a manipulator is redundant relative to its task, only a single joint failure occurs at any given time, the manipulator is capable of detecting a joint failure and immediately locks the failed joint, and the environment is static and known. The algorithm is evaluated on a three degree-of-freedom planar manipulator for a total of eleven thousand different scenarios, randomly varying the robot's start and goal positions and the number and locations of obstacles in the environment. Statistical data are presented related to the computation time required by the different steps of the algorithm as a function of the complexity of the environment

Quadtree-based eigendecomposition for pose estimation in the presence of occlusion and background clutter

Includes bibliographical references (pages 29-30).Eigendecomposition-based techniques are popular for a number of computer vision problems, e.g., object and pose estimation, because they are purely appearance based and they require few on-line computations. Unfortunately, they also typically require an unobstructed view of the object whose pose is being detected. The presence of occlusion and background clutter precludes the use of the normalizations that are typically applied and significantly alters the appearance of the object under detection. This work presents an algorithm that is based on applying eigendecomposition to a quadtree representation of the image dataset used to describe the appearance of an object. This allows decisions concerning the pose of an object to be based on only those portions of the image in which the algorithm has determined that the object is not occluded. The accuracy and computational efficiency of the proposed approach is evaluated on 16 different objects with up to 50% of the object being occluded and on images of ships in a dockyard

Analysis of eigendecomposition for sets of correlated images at different resolutions

Includes bibliographical references.Eigendecomposition is a common technique that is performed on sets of correlated images in a number of computer vision and robotics applications. Unfortunately, the computation of an eigendecomposition can become prohibitively expensive when dealing with very high resolution images. While reducing the resolution of the images will reduce the computational expense, it is not known how this will affect the quality of the resulting eigendecomposition. The work presented here proposes a framework for quantifying the effects of varying the resolution of images on the eigendecomposition that is computed from those images. Preliminary results show that an eigendecomposition from low-resolution images may be nearly as effective in some applications as those from high-resolution images.This work was supported by the National Imagery and Mapping Agency under contract no. NMA201-00-1-1003 and through collaborative participation in the Robotics Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0012

Radiative transfer in disc galaxies -- III. The observed kinematics of dusty disc galaxies

We present SKIRT (Stellar Kinematics Including Radiative Transfer), a new Monte Carlo radiative transfer code that allows the calculation of the observed stellar kinematics of a dusty galaxy. The code incorporates the effects of both absorption and scattering by interstellar dust grains, and calculates the Doppler shift of the emerging radiation exactly by taking into account the velocities of the emitting stars and the individual scattering dust grains. The code supports arbitrary distributions of dust through a cellular approach, whereby the integration through the dust is optimized by means of a novel efficient trilinear interpolation technique. We apply our modelling technique to calculate the observed kinematics of realistic models for dusty disc galaxies. We find that the effects of dust on the mean projected velocity and projected velocity dispersion are severe for edge-on galaxies. For galaxies which deviate more than a few degrees from exactly edge-on, the effects are already strongly reduced. As a consequence, dust attenuation cannot serve as a possible way to reconcile the discrepancy between the observed shallow slopes of the inner rotation curves of LSB galaxies and the predictions of CDM cosmological models. For face-on galaxies, the velocity dispersion increases with increasing dust mass due to scattering, but the effects are limited, even for extended dust distributions. Finally, we show that serious errors can be made when the individual velocities of the dust grains are neglected in the calculations.Comment: 14 pages, 6 figures, accepted for publication in MNRA